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" The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth ; if the multiple... "
The definitions, postulates, axioms, and enunciations of the propositions of ... - Pagina 23
di Euclides - 1848 - 42 pagine
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Elementary algebra: with brief notices of its history

Robert Potts - 1879 - 672 pagine
...are proportionals by Eue. V., def. 5, ' namely : — | The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever...
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Military examinations. Mathematical examination papers, set at entrance to ...

Sandhurst roy. military coll - 1880 - 68 pagine
...and hexagon. 7. Give Euclid's definition of ratio. When is the first of four magnitudes said to have the same ratio to the second which the third has to the fourth ? 8. The sides about the equal angles of equiangular triangles are proportional. If a straight line...
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The Elements of Euclid for the Use of Schools and Colleges: With Notes, an ...

Isaac Todhunter - 1880 - 426 pagine
...together. [V. Definition 5. Wherefore, if any number &c. Q.EJ>. PROPOSITION 13. THEOREM. If the first have the same ratio to the second which the third has to the fourth, but the third to the fourth a greater ratio than the fifth to the si.cth, thefirst shall have to ths...
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Elements of Geometry

George Albert Wentworth - 1881 - 266 pagine
...DEP. Euclid's test of a proportion is as follows : — "The first of four magnitudes is said to have the same ratio to the second which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever...
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1881 - 236 pagine
...a greater ratio to the seccond, than the fifth lias to the sixth. PROP. XIV. THEOREM. If the first has the same ratio to the second which the third has to *>u. fourth ; and if the first be greater than the third, the second is greater than the fourth ; if...
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Elementary algebra. To which is now added an appendix

James Hamblin Smith - 1883 - 466 pagine
...is given in Book v. Def. 5, where it stands thus : \ " The first of four magnitudes is said to have the same ratio to the second which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken and any equimultiples whatsoever...
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Notes on algebra

Howard Candler - 1885 - 116 pagine
...proportionals if — = b а The geometrical definition is 2. The first of four magnitudes is said to have the same ratio to the second which the third has to the fourth, when, any equimultiples whatever being taken of the ist and 3rd, and any equimultiples whatever of...
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The Teaching of Elementary Mathematics

David Eugene Smith - 1900 - 338 pagine
...definition of equal ratios to be assured of this fact : " The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever...
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Ellen: Or, Whisperings of an Old Pine, Volume 1

Joseph Battell - 1903 - 722 pagine
...contains 2 three times; then 1 8 must contain 2, 3 X 3, or 9 times. See Axiom 6. PROPOSITION IV. ' If the first of four magnitudes has the same ratio to the second which the third has to the fourth, and if any equimultiple whatever is taken of the first and third, and any whatever of the second and...
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First Stage Practical Plane and Solid Geometry

G. F. Burn - 1903 - 272 pagine
...proportion is the equality of two ratios. Four quantities are therefore in true proportion when the first has the same ratio to the second which the third has to the fourth ; thus, since 3 : 6 and 1 : 2 are equal ratios, we have a true proportion in 3 : 6 : : 1 : 2 (read...
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